Describe a use for the Remainder Theorem.

Describe a use for the Remainder Theorem.

Question
Polynomial division
asked 2021-03-08
Describe a use for the Remainder Theorem.

Answers (1)

2021-03-09
Concept used:
Remainder theorem states that “If a polynomial f(x)is divided by x — k, then the remainder is the value f(k)”
We can use polynomial division to evaluate polynomials using the Remainder Theorem. If the polynomial is divided by x - k, the remainder is r, then this value equals the value of the polynomial function at k, that is, f(k). So this helps to evaluate the polynomial at a given value of x. Since the division is done by a linear factor, we can use the synthetic division method.
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\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}}}}\)
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Use long division to rewrite the equation for g in the form
\(\text{quotient}+\frac{remainder}{divisor}\)
Then use this form of the function's equation and transformations of
\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}}}}\)
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\(\displaystyle{g{{\left({x}\right)}}}={\frac{{{3}{x}-{7}}}{{{x}-{2}}}}\)

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